Add helper for checking local peers

[AlekSi]

Description

Plus some small fixes.

Readiness checklist

• I added/updated unit tests (and they pass).
• I added/updated integration/compatibility tests (and they pass).
• I added/updated comments and checked rendering.
• I made spot refactorings.
• I updated user documentation.
• I ran task all, and it passed.
• I ensured that PR title is good enough for the changelog.
• (for maintainers only) I set Reviewers (@FerretDB/core), Milestone (Next), Labels, Project and project's Sprint fields.
• I marked all done items in this checklist.

[AlekSi]

Oops!

[chilagrow]

Ouch

[codecov]

Codecov Report

Attention: Patch coverage is 75.00000% with 2 lines in your changes are missing coverage. Please review.

Project coverage is 73.78%. Comparing base (892780a) to head (ec0bc37).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4159      +/-   ##
==========================================
- Coverage   74.31%   73.78%   -0.53%     
==========================================
  Files         353      353              
  Lines       22789    22793       +4     
==========================================
- Hits        16935    16818     -117     
- Misses       4556     4694     +138     
+ Partials     1298     1281      -17     

Files	Coverage Δ
ferretdb/ferretdb.go	86.51% <ø> (ø)
integration/setup/setup.go	81.25% <ø> (ø)
internal/clientconn/conninfo/conn_info.go	96.55% <100.00%> (+0.12%)	⬆️
internal/handler/msg_whatsmyuri.go	100.00% <100.00%> (ø)
internal/clientconn/conn.go	51.35% <33.33%> (-0.35%)	⬇️

... and 11 files with indirect coverage changes

Flag	Coverage Δ
filter-true	67.21% <50.00%> (-0.63%)	⬇️
hana-1	?
integration	67.21% <50.00%> (-0.63%)	⬇️
mongodb-1	4.87% <0.00%> (-0.01%)	⬇️
postgresql-1	48.45% <25.00%> (+0.02%)	⬆️
postgresql-2	51.26% <37.50%> (+4.07%)	⬆️
postgresql-3	49.47% <12.50%> (-0.01%)	⬇️
sqlite-1	47.53% <25.00%> (+0.02%)	⬆️
sqlite-2	?
sqlite-3	48.58% <12.50%> (+0.01%)	⬆️
unit	32.49% <25.00%> (+<0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

[chilagrow]

Thanks for this!